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rSPECMICP SpecMiCP / ReactMiCP
saturation_equation.cpp
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/*-------------------------------------------------------------------------------
Copyright (c) 2014,2015 F. Georget <fabieng@princeton.edu>, Princeton University
All rights reserved.
Redistribution and use in source and binary forms, with or without modification,
are permitted provided that the following conditions are met:
1. Redistributions of source code must retain the above copyright notice, this
list of conditions and the following disclaimer.
2. Redistributions in binary form must reproduce the above copyright notice,
this list of conditions and the following disclaimer in the documentation and/or
other materials provided with the distribution.
3. Neither the name of the copyright holder nor the names of its contributors
may be used to endorse or promote products derived from this software without
specific prior written permission.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR
ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
-----------------------------------------------------------------------------*/
#include "saturation_equation.hpp"
#include "variables_box.hpp"
#include "transport_constraints.hpp"
#include "../../../dfpm/meshes/mesh1d.hpp"
#include "../../../dfpmsolver/parabolic_driver.hpp"
#include "../../../utils/compat.hpp"
#include <vector>
namespace
specmicp
{
namespace
dfpmsolver
{
// explicit template instanciation
template
class
dfpmsolver
::
ParabolicDriver
<
reactmicp
::
systems
::
unsaturated
::
SaturationEquation
>
;
}
//end namespace dfpmsolver
}
//end namespace specmicp
namespace
specmicp
{
namespace
reactmicp
{
namespace
systems
{
namespace
unsaturated
{
static
constexpr
index_t
no_equation
{
-
1
};
static
constexpr
index_t
no_eq_no_var
{
-
2
};
static
constexpr
index_t
not_initialized
{
-
5
};
struct
SPECMICP_DLL_LOCAL
SaturationEquation
::
SaturationEquationImpl
{
mesh
::
Mesh1DPtr
m_mesh
;
SaturationVariableBox
m_vars
;
std
::
vector
<
index_t
>
m_ideq
;
bool
m_store_residual_info
;
scalar_t
m_scaling
{
1.0
};
SaturationEquationImpl
(
mesh
::
Mesh1DPtr
the_mesh
,
SaturationVariableBox
vars
)
:
m_mesh
(
the_mesh
),
m_vars
(
vars
),
m_ideq
(
the_mesh
->
nb_nodes
(),
not_initialized
)
{}
index_t
&
id_equation
(
index_t
node
)
{
return
m_ideq
[
node
];}
bool
node_can_flux
(
index_t
node
)
{
return
m_ideq
[
node
]
!=
no_eq_no_var
;}
bool
node_has_eq
(
index_t
node
)
{
return
m_ideq
[
node
]
>
no_equation
;}
void
set_store_residual_info
()
{
m_store_residual_info
=
true
;
}
void
reset_store_residual_info
()
{
m_store_residual_info
=
false
;
}
bool
store_residual_info
()
{
return
m_store_residual_info
;
}
//! \brief Return a pointer to the mesh
mesh
::
Mesh1D
*
mesh
()
{
return
m_mesh
.
get
();}
range_t
range_nodes
()
{
return
m_mesh
->
range_nodes
();}
void
set_relative_variables
(
const
Vector
&
displacement
);
void
set_relative_variables
(
index_t
node
,
const
Vector
&
displacement
);
void
compute_transport_rate
(
scalar_t
dt
,
const
Vector
&
displacement
);
};
SaturationEquation
::~
SaturationEquation
()
=
default
;
SaturationEquation
::
SaturationEquation
(
mesh
::
Mesh1DPtr
the_mesh
,
SaturationVariableBox
&
variables
,
const
TransportConstraints
&
constraints
)
:
m_neq
(
-
1
),
m_tot_ndf
(
the_mesh
->
nb_nodes
()),
m_impl
(
make_unique
<
SaturationEquationImpl
>
(
the_mesh
,
variables
))
{
number_equations
(
constraints
);
}
void
SaturationEquation
::
number_equations
(
const
TransportConstraints
&
constraints
)
{
for
(
index_t
node:
constraints
.
fixed_nodes
())
{
m_impl
->
id_equation
(
node
)
=
no_equation
;
}
for
(
index_t
node:
constraints
.
gas_nodes
())
{
m_impl
->
id_equation
(
node
)
=
no_eq_no_var
;
}
index_t
neq
=
0
;
for
(
index_t
node:
m_impl
->
range_nodes
())
{
if
(
m_impl
->
id_equation
(
node
)
==
not_initialized
)
{
m_impl
->
id_equation
(
node
)
=
neq
;
++
neq
;
}
}
m_neq
=
neq
;
}
index_t
SaturationEquation
::
id_equation
(
index_t
id_dof
)
{
return
m_impl
->
id_equation
(
id_dof
)
<
0
?
no_equation:
m_impl
->
id_equation
(
id_dof
);
}
void
SaturationEquation
::
set_scaling
(
scalar_t
value
)
{
m_impl
->
m_scaling
=
value
;
}
// Residuals
// =========
void
SaturationEquation
::
residuals_element
(
index_t
element
,
const
Vector
&
displacement
,
const
Vector
&
velocity
,
Eigen
::
Vector2d
&
element_residual
,
bool
use_chemistry_rate
)
{
element_residual
.
setZero
();
mesh
::
Mesh1D
*
m_mesh
=
m_impl
->
mesh
();
SaturationVariableBox
&
vars
=
m_impl
->
m_vars
;
const
scalar_t
mass_coeff_0
=
m_mesh
->
get_volume_cell_element
(
element
,
0
);
const
scalar_t
mass_coeff_1
=
m_mesh
->
get_volume_cell_element
(
element
,
1
);
const
index_t
node_0
=
m_mesh
->
get_node
(
element
,
0
);
const
index_t
node_1
=
m_mesh
->
get_node
(
element
,
1
);
scalar_t
flux_0
=
0.0
;
scalar_t
flux_1
=
0.0
;
if
(
m_impl
->
node_can_flux
(
node_0
)
and
m_impl
->
node_can_flux
(
node_1
))
{
// Cap pressure gradient
const
scalar_t
perm_0
=
vars
.
liquid_permeability
(
node_0
)
*
vars
.
relative_liquid_permeability
(
node_0
);
const
scalar_t
perm_1
=
vars
.
liquid_permeability
(
node_1
)
*
vars
.
relative_liquid_permeability
(
node_1
);
const
scalar_t
perm
=
2.0
/
(
1.0
/
perm_0
+
1.0
/
perm_1
);
const
scalar_t
aq_coefficient
=
(
vars
.
aqueous_concentration
(
node_0
)
+
vars
.
aqueous_concentration
(
node_1
)
)
/
2.0
;
const
scalar_t
cap_pressure_gradient
=
(
vars
.
capillary_pressure
(
node_1
)
-
vars
.
capillary_pressure
(
node_0
)
)
/
m_mesh
->
get_dx
(
element
);
const
scalar_t
advection_flux
=
(
perm
/
vars
.
constants
.
viscosity_liquid_water
)
*
cap_pressure_gradient
;
const
scalar_t
cappres_flux
=
-
aq_coefficient
*
advection_flux
;
// Diffusion Cw
const
scalar_t
coeff_diff_0
=
vars
.
liquid_diffusivity
(
node_0
)
*
vars
.
relative_liquid_diffusivity
(
node_0
);
const
scalar_t
coeff_diff_1
=
vars
.
liquid_diffusivity
(
node_1
)
*
vars
.
relative_liquid_diffusivity
(
node_1
);
const
scalar_t
coeff_diff
=
2.0
/
(
1.0
/
coeff_diff_0
+
1.0
/
coeff_diff_1
);
const
scalar_t
aq_flux
=
coeff_diff
*
(
vars
.
aqueous_concentration
(
node_1
)
-
vars
.
aqueous_concentration
(
node_0
)
)
/
m_mesh
->
get_dx
(
element
);
// Tot flux
const
scalar_t
tot_flux
=
m_mesh
->
get_face_area
(
element
)
*
(
cappres_flux
+
aq_flux
);
flux_0
=
tot_flux
;
flux_1
=
-
tot_flux
;
// Storage
if
(
m_impl
->
store_residual_info
())
{
// advective flux stored by element
vars
.
advection_flux
(
element
)
=
advection_flux
;
// fluxes to compute exchange term
vars
.
liquid_saturation
.
transport_fluxes
(
node_0
)
+=
flux_0
;
vars
.
liquid_saturation
.
transport_fluxes
(
node_1
)
+=
flux_1
;
}
}
// transient
if
(
m_impl
->
node_has_eq
(
node_0
))
{
const
scalar_t
porosity_0
=
vars
.
porosity
(
node_0
);
const
scalar_t
aq_tot_conc_0
=
vars
.
aqueous_concentration
(
node_0
);
const
scalar_t
saturation_0
=
displacement
(
node_0
);
scalar_t
transient_0
=
(
porosity_0
*
aq_tot_conc_0
*
velocity
(
node_0
)
+
saturation_0
*
aq_tot_conc_0
*
vars
.
porosity
.
velocity
(
node_0
)
+
porosity_0
*
saturation_0
*
vars
.
aqueous_concentration
.
velocity
(
node_0
)
);
auto
res
=
mass_coeff_0
*
transient_0
-
flux_0
;
if
(
use_chemistry_rate
)
{
const
scalar_t
chemistry_0
=
vars
.
liquid_saturation
.
chemistry_rate
(
node_0
)
+
vars
.
solid_concentration
.
chemistry_rate
(
node_0
)
+
vars
.
vapor_pressure
.
chemistry_rate
(
node_0
)
;
res
-=
mass_coeff_0
*
chemistry_0
;
}
element_residual
(
0
)
=
res
/
m_impl
->
m_scaling
;
}
if
(
m_impl
->
node_has_eq
(
node_1
))
{
const
scalar_t
porosity_1
=
vars
.
porosity
(
node_1
);
const
scalar_t
aq_tot_conc_1
=
vars
.
aqueous_concentration
(
node_1
);
const
scalar_t
saturation_1
=
displacement
(
node_1
);
scalar_t
transient_1
=
(
porosity_1
*
aq_tot_conc_1
*
velocity
(
node_1
)
+
saturation_1
*
aq_tot_conc_1
*
vars
.
porosity
.
velocity
(
node_1
)
+
porosity_1
*
saturation_1
*
vars
.
aqueous_concentration
.
velocity
(
node_1
)
);
auto
res
=
mass_coeff_1
*
transient_1
-
flux_1
;
if
(
use_chemistry_rate
)
{
const
scalar_t
chemistry_1
=
vars
.
liquid_saturation
.
chemistry_rate
(
node_1
)
+
vars
.
solid_concentration
.
chemistry_rate
(
node_1
)
+
vars
.
vapor_pressure
.
chemistry_rate
(
node_1
)
;
res
-=
mass_coeff_1
*
chemistry_1
;
}
element_residual
(
1
)
=
res
/
m_impl
->
m_scaling
;
}
}
//! \brief Compute the residuals
void
SaturationEquation
::
compute_residuals
(
const
Vector
&
displacement
,
const
Vector
&
velocity
,
Vector
&
residuals
,
bool
use_chemistry_rate
)
{
mesh
::
Mesh1D
*
m_mesh
=
m_impl
->
mesh
();
residuals
.
setZero
(
get_neq
());
m_impl
->
set_store_residual_info
();
set_relative_variables
(
displacement
);
Eigen
::
Vector2d
element_residual
;
for
(
index_t
element:
m_mesh
->
range_elements
())
{
residuals_element
(
element
,
displacement
,
velocity
,
element_residual
,
use_chemistry_rate
);
const
index_t
node_0
=
m_mesh
->
get_node
(
element
,
0
);
if
(
m_impl
->
node_has_eq
(
node_0
))
{
residuals
(
m_impl
->
id_equation
(
node_0
))
+=
element_residual
(
0
);
}
const
index_t
node_1
=
m_mesh
->
get_node
(
element
,
1
);
if
(
m_impl
->
node_has_eq
(
node_1
))
{
residuals
(
m_impl
->
id_equation
(
node_1
))
+=
element_residual
(
1
);
}
}
m_impl
->
reset_store_residual_info
();
}
void
SaturationEquation
::
compute_jacobian
(
Vector
&
displacement
,
Vector
&
velocity
,
Eigen
::
SparseMatrix
<
scalar_t
>&
jacobian
,
scalar_t
alphadt
)
{
mesh
::
Mesh1D
*
m_mesh
=
m_impl
->
mesh
();
dfpm
::
list_triplet_t
jacob
;
const
index_t
estimation
=
3
*
get_neq
();
jacob
.
reserve
(
estimation
);
// assume relative variables are set
for
(
index_t
element:
m_mesh
->
range_elements
())
{
Eigen
::
Vector2d
element_residual_orig
;
residuals_element
(
element
,
displacement
,
velocity
,
element_residual_orig
,
false
);
for
(
index_t
enodec
=
0
;
enodec
<
2
;
++
enodec
)
{
const
index_t
nodec
=
m_mesh
->
get_node
(
element
,
enodec
);
if
(
not
m_impl
->
node_has_eq
(
nodec
))
continue
;
const
scalar_t
tmp_d
=
displacement
(
nodec
);
const
scalar_t
tmp_v
=
velocity
(
nodec
);
scalar_t
h
=
eps_jacobian
*
std
::
abs
(
tmp_v
);
if
(
h
<
1e-4
*
eps_jacobian
)
h
=
eps_jacobian
;
velocity
(
nodec
)
=
tmp_v
+
h
;
h
=
velocity
(
nodec
)
-
tmp_v
;
displacement
(
nodec
)
=
tmp_d
+
alphadt
*
h
;
m_impl
->
set_relative_variables
(
nodec
,
displacement
);
Eigen
::
Vector2d
element_residual
;
residuals_element
(
element
,
displacement
,
velocity
,
element_residual
,
false
);
displacement
(
nodec
)
=
tmp_d
;
velocity
(
nodec
)
=
tmp_v
;
m_impl
->
set_relative_variables
(
nodec
,
displacement
);
for
(
index_t
enoder
=
0
;
enoder
<
2
;
++
enoder
)
{
const
index_t
noder
=
m_mesh
->
get_node
(
element
,
enoder
);
if
(
not
m_impl
->
node_has_eq
(
noder
))
continue
;
jacob
.
push_back
(
dfpm
::
triplet_t
(
m_impl
->
id_equation
(
noder
),
m_impl
->
id_equation
(
nodec
),
(
element_residual
(
enoder
)
-
element_residual_orig
(
enoder
))
/
h
));
}
}
}
jacobian
=
Eigen
::
SparseMatrix
<
scalar_t
>
(
get_neq
(),
get_neq
());
jacobian
.
setFromTriplets
(
jacob
.
begin
(),
jacob
.
end
());
}
void
SaturationEquation
::
update_solution
(
const
Vector
&
update
,
scalar_t
lambda
,
scalar_t
alpha_dt
,
Vector
&
predictor
,
Vector
&
displacement
,
Vector
&
velocity
)
{
for
(
index_t
node:
m_impl
->
mesh
()
->
range_nodes
())
{
if
(
m_impl
->
node_has_eq
(
node
))
{
velocity
(
node
)
+=
lambda
*
update
(
m_impl
->
id_equation
(
node
));
}
}
displacement
=
predictor
+
alpha_dt
*
velocity
;
m_impl
->
compute_transport_rate
(
alpha_dt
,
displacement
);
}
void
SaturationEquation
::
set_relative_variables
(
const
Vector
&
displacement
)
{
return
m_impl
->
set_relative_variables
(
displacement
);
}
void
SaturationEquation
::
SaturationEquationImpl
::
set_relative_variables
(
index_t
node
,
const
Vector
&
displacement
)
{
if
(
not
node_can_flux
(
node
))
return
;
const
scalar_t
saturation
=
displacement
(
node
);
m_vars
.
relative_liquid_diffusivity
(
node
)
=
m_vars
.
relative_liquid_diffusivity_f
(
node
,
saturation
);
m_vars
.
relative_liquid_permeability
(
node
)
=
m_vars
.
relative_liquid_permeability_f
(
node
,
saturation
);
m_vars
.
capillary_pressure
(
node
)
=
m_vars
.
capillary_pressure_f
(
node
,
saturation
);
}
void
SaturationEquation
::
SaturationEquationImpl
::
set_relative_variables
(
const
Vector
&
displacement
)
{
for
(
index_t
node:
m_mesh
->
range_nodes
())
{
set_relative_variables
(
node
,
displacement
);
}
}
void
SaturationEquation
::
SaturationEquationImpl
::
compute_transport_rate
(
scalar_t
dt
,
const
Vector
&
displacement
)
{
MainVariable
&
saturation
=
m_vars
.
liquid_saturation
;
const
MainVariable
&
solid_conc
=
m_vars
.
solid_concentration
;
const
MainVariable
&
pressure
=
m_vars
.
vapor_pressure
;
const
SecondaryTransientVariable
&
porosity
=
m_vars
.
porosity
;
const
SecondaryTransientVariable
&
aqueous_concentration
=
m_vars
.
aqueous_concentration
;
for
(
index_t
node:
m_mesh
->
range_nodes
())
{
if
(
!
node_has_eq
(
node
))
continue
;
const
scalar_t
transient
=
(
(
porosity
(
node
)
*
aqueous_concentration
(
node
)
*
displacement
(
node
))
-
(
porosity
.
predictor
(
node
)
*
aqueous_concentration
.
predictor
(
node
)
*
saturation
.
predictor
(
node
))
)
/
dt
;
const
scalar_t
chem_rates
=
(
saturation
.
chemistry_rate
(
node
)
+
solid_conc
.
chemistry_rate
(
node
)
+
pressure
.
chemistry_rate
(
node
)
);
saturation
.
transport_fluxes
(
node
)
=
transient
-
chem_rates
;
}
}
}
//end namespace unsaturated
}
//end namespace systems
}
//end namespace reactmicp
}
//end namespace specmicp
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